In this subsection, we briefly explain the implications of the smooth function model for self-normalized sums, which we use in the proof of t.llt. For a more detailed introduction, see [1]}. Let \(Y_j:=(X_j,X_j^2)\)  with mean \(\mu _Y=(0,1)\)  and covariance matrix
\(\Sigma := \mathop {\mathrm {Cov}}(Y)=\begin{pmatrix}1 & \mu _3\\\mu _3 & \mu _4-1\end{pmatrix}.\) 
